Question

For rectangles with the same area, the length varies inversely

as the width. One rectangle has a length of 12 cm and a
width of 5 cm. Find the length of another rectangle with the
same area whose width is 4 cm.

Answer 1

To find the length of another rectangle with the same area as the given rectangle, we can set up a proportion between the lengths and widths of the two rectangles. The length of another rectangle with the same area, whose width is 4 cm, is 9.6 cm.

Step-by-step explanation:

To find the length of another rectangle with the same area as the given rectangle, we can set up a proportion between the lengths and widths of the two rectangles.

We know that for rectangles with the same area, the length varies inversely as the width. So, we can set up the proportion:

Length of rectangle 1 / Width of rectangle 1 = Length of rectangle 2 / Width of rectangle 2

Plugging in the values, we get:

12 cm / 5 cm = Length of rectangle 2 / 4 cm

Cross-multiplying, we get:

12 cm * 4 cm = 5 cm * Length of rectangle 2

Simplifying, we find:

48 cm = 5 cm * Length of rectangle 2

Dividing both sides by 5 cm, we get:

Length of rectangle 2 = 48 cm / 5 cm = 9.6 cm

Therefore, the length of another rectangle with the same area, whose width is 4 cm, is 9.6 cm.